Problem: Simplify the following expression: $\dfrac{35n}{14n^4}$ You can assume $n \neq 0$.
$ \dfrac{35n}{14n^4} = \dfrac{35}{14} \cdot \dfrac{n}{n^4} $ To simplify $\frac{35}{14}$ , find the greatest common factor (GCD) of $35$ and $14$ $35 = 5 \cdot 7$ $14 = 2 \cdot 7$ $ \mbox{GCD}(35, 14) = 7 $ $ \dfrac{35}{14} \cdot \dfrac{n}{n^4} = \dfrac{7 \cdot 5}{7 \cdot 2} \cdot \dfrac{n}{n^4} $ $\phantom{ \dfrac{35}{14} \cdot \dfrac{1}{4}} = \dfrac{5}{2} \cdot \dfrac{n}{n^4} $ $ \dfrac{n}{n^4} = \dfrac{n}{n \cdot n \cdot n \cdot n} = \dfrac{1}{n^3} $ $ \dfrac{5}{2} \cdot \dfrac{1}{n^3} = \dfrac{5}{2n^3} $